Your "tow rating" of #5500 is with an empty truck and does not include any additional payload to the truck. Well, other than maybe the driver and a full tank of gas... Is that how you plan on traveling?? ;)
So, lets say you load your truck up with the family and some stuff in the bed.. That will mean you basically have to reduce that "tow rating" by what you just loaded into the truck..
That is, if you want to still stay within the other trucks weight ratings of GVWR and front/rear GAWR.. Payload figures did not exist for your 2003, but it is essentially what your truck actually weighs subtracted from it's GVWR.
I've got a 22', #5000 GVWR TT that had a "dry weight" of around #3400.. It weighs every bit of that #5000 GVWR now.. I know, I've weighed it.. :)
Anyway, shopping by trailers "dry weight" and comparing that to the trucks "tow rating" is fine if you leave enough room between the two, but get too close, and something is going to be overweight in the end..
Good luck!
Mitch